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arXiv · 2501.19189

Rationality and categorical properties of the moduli of instanton bundles on the projective 3-space

Mihai Halic·Roshan Tajarod
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Abstract

We prove the rationality and irreducibility of the moduli space of mathematical instanton vector bundles of arbitrary rank and charge on $\mathbb P^3$. In particular, the result applies to the rank-2 case. This problem was first studied by Barth, Ellingsrud-Stromme, Hartshorne, Hirschowitz-Narasimhan in the late 1970s. We also show that the mathematical instantons of variable rank and charge form a monoidal category. The proof is based on an in-depth analysis of the Barth-Hulek monad-construction and on a detailed description of the moduli space of (framed and unframed) stable bundles on Hirzebruch surfaces.

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BibTeXRIS

Mihai Halic, Roshan Tajarod. 2025-05-05. Rationality and categorical properties of the moduli of instanton bundles on the projective 3-space. https://arxiv.org/abs/2501.19189

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